An RCD space with parameters 
and 
is a complete separable
geodesic metric measure
space satisfying the unreduced curvature-dimension
condition 
and having quadratic Cheeger energy. The reference
measure has full support
and is finite on bounded sets.
The acronym expresses a Riemannian curvature-dimension
condition. For example, Euclidean 
-space with Lebesgue measure
satisfies 
for 
. The space is noncollapsed in
dimension 
when its reference measure is
exactly its 
-dimensional
Hausdorff measure, rather than merely an equivalent
measure.
RCD Space
See also
Alexandrov Space, Cheeger Energy, Curvature-Dimension Condition, Distributional Hessian, Metric Measure SpaceExplore with Wolfram|Alpha
References
Ambrosio, L.; Gigli, N.; and Savaré, G. "Metric Measure Spaces with Riemannian Ricci Curvature Bounded from Below." Duke Math. J. 163, 1405-1490, 2014. https://doi.org/10.1215/00127094-2681605.De Philippis, G. and Gigli, N. "Non-Collapsed Spaces with Ricci Curvature Bounded from Below." J. École Polytech. Math. 5, 613-650, 2018. https://doi.org/10.5802/jep.80.Sturm, K.-T. "On the Geometry of Metric Measure Spaces. II." Acta Math. 196, 133-177, 2006. https://doi.org/10.1007/s11511-006-0003-7.Cite this as:
Weisstein, Eric W. "RCD Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RCDSpace.html